The present invention relates to systems and methods for determining the wave speed of a medium and more particularly to an inverse tomographic technique therefor.
The term tomography generally denotes the cross-sectional imaging of an object from either transmission or reflected data collected by illuminating the object from several different directions. Accordingly, inverse tomography involves transmitting signals through a medium and inferring the wave speed in the medium by examining detected signals.
The ocean has been extensively studied and mapped. However, most studies depend on knowledge of the actual sound speed in the ocean. Therefore, it is critical to have accurate knowledge of the sound speed of a region under consideration, so that knowledge of the structure of the region may also be accurate. Furthermore, the accuracy of sonar depends on the accuracy of knowledge about the ocean water sound speed. Similarly, knowledge of geological formations depends on measurements based on accurate knowledge of wave speed.
Techniques utilized in the past have shown that remote sensing of ocean mesoscale structures is highly effective at ranges up to 1000 km using high frequencies (above 100 Hz) where sound-speed structure is inverted (that is, determined) through comparison of measured with predicted times of arrival of rays/multipaths transmitted from a pulsed source and propagating to a detector. These approaches use either moored transmitter/detectors, or moving transmitter/detectors and involve computation in the time domain. In other words, these approaches involve calculation of the elapsed time between emission and receipt of signals. The detectors, whether moored or moving, are vertical hydrophone arrays, thus having multiple sensors.
The moored tomography technique requires resolution on the order of 10 msec. to detect the effects of environmental changes, and this demands broadband coded source signals with accurate synchronization of transmission and recordings. The data must be collected over long periods of time to counter fluctuations due to internal waves, tides, movement of fish and other material in the medium, and other environmental conditions. The location of the sources and detectors must be known precisely. The moored approach suffers from a sparsity of transmitters and detectors since deploying them is expensive. On the other hand, moving the transmitters and detectors, usually by ship, is time consuming and costly.
It would be desirable to use a number of fast, inexpensive air deployed explosives with high signal to noise ratio as the sources. However, these sources cannot be used with the above techniques because they do not provide precisely known times and locations, nor do they provide precisely known waveforms for the signals transmitted.
It would also be desirable to perform the calculations in the frequency domain with low frequencies, thus minimizing the sensitivity to environmental fluctuations and eliminating the necessity of knowing the precise locations for the sources and detectors, since the accuracy needed would depend on the wavelength, which would be longer. However, the above techniques use the time domain and require frequencies of about 100 Hz.
U.S. Pat. No. 4,995,001 to John L. Spiesberger discloses a method for determining, inter alia, the speed of propagation of a signal in a medium, where the medium is not necessarily ocean water and the signal is not necessarily acoustic. The method uses calculations in the time domain and uses moored transmissions. As with the above methods for use in ocean mesoscale structural determination, it provides relatively inaccurate results or requires the use of accurate data.
Matched field processing, examples of which include Capon processing, maximum likelihood, minimum variance, linear processing, and maximum entropy, has been used to locate sources. It involves cross-correlating, that is, comparing or matching actual measured data from signals, with theoretical predictions of the measured data, based on acoustic fields according to a particular propagation model, to obtain matched field processing power. Further explanation and details of matched field processing power are found in Bucker, H. P. (1976), "Use of Calculated Sound Fields and Matched-Field Detection to Locate Sound Sources in Shallow Water," J. Acoust. Soc. Am. 59, 368-373; Fizell, R. G., "Application of High-Resolution Processing to Range and Depth Estimation Using Ambiguity Function Methods," J. Acoust. Soc. Am. 82, 606-613, which are incorporated herein by reference. Matched field processing of interest herein is in the frequency domain.
The ocean is known to have sound speed profiles. In other words, it is known that the sound speed varies with depth because of factors such as temperature, pressure and salinity. FIG. 1 shows an example of a sound speed profile. However, the sound speed profile might vary with range. Accordingly, the region under consideration is partitioned into a discrete set of cells so that the sound speed profile can be determined at each cell.
Because the maximum sound speed is generally higher on the surface and in deep water, sound speed typically reaches a minimum at depths of about 500-1000 m, sound propagated horizontally will generally refract vertically and reflect from the surface, as shown in FIG. 2.
In order to reduce the parameter search space for determining the sound speed profile in each cell, wave speeds can be represented by a linear combination of known linearly independent functions, a basis. In other words, ##EQU1## For empirical orthogonal functions (E.O.F.s), the functions f.sub.j are eigenfunctions of a particular known covariance matrix. Since the functions f.sub.j are readily determined from air-deployed expendable bathythermograph data (A.X.B.T.), conductivity, temperature and depth (C.T.D.), or archival data, the problem of determining sound speed profiles which best match the measured data reduces to finding the coefficients .alpha..sub.j for all cells and all values of j, which coefficient values maximize the matched field processing power. However, with this linear representation of wave speed, it is very cumbersome and inefficient to calculate the predicted acoustic fields, on which calculation of the matched field processing power is based.
Even if an efficient method of calculating the predicted acoustic fields and therefore matched field processing power were found, the problem of solving for coefficients which maximize the matched field processing power remains. Calculations using standard numerical schemes, including simulated annealing, are prohibitively time consuming. Even medical tomography backpropagation techniques, which involve considering many paths through a cell of interest, and weighting the paths equally, lead to inaccurate results.